Abstract
For a bounded linear operator T one considers questions regarding the commutativity of the commutant {T}′, the possibility of approximation in the weak operator topology of the operators from the bicommutant {T}″, reflexivity, the equality of other operator algebras and lattices of subspaces, connected with the operator T. One gives the answers to these questions for operators from certain classes (Co-contractions; weak contractions, contractions having finite defect index, etc.).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 178, pp. 23–56, 1989.
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Kapustin, V.V., Lipin, A.V. Operator algebras and lattices of invariant subspaces. I. J Math Sci 61, 1963–1981 (1992). https://doi.org/10.1007/BF01095662
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DOI: https://doi.org/10.1007/BF01095662